Multivariate analysis for selecting animals for experimental research

Background Several researchers seek methods for the selection of homogeneous groups of animals in experimental studies, a fact justified because homogeneity is an indispensable prerequisite for casualization of treatments. The lack of robust methods that comply with statistical and biological principles is the reason why researchers use empirical or subjective methods, influencing their results. Objective To develop a multivariate statistical model for the selection of a homogeneous group of animals for experimental research and to elaborate a computational package to use it. Methods The set of echocardiographic data of 115 male Wistar rats with supravalvular aortic stenosis (AoS) was used as an example of model development. Initially, the data were standardized, and became dimensionless. Then, the variance matrix of the set was submitted to principal components analysis (PCA), aiming at reducing the parametric space and at retaining the relevant variability. That technique established a new Cartesian system into which the animals were allocated, and finally the confidence region (ellipsoid) was built for the profile of the animals’ homogeneous responses. The animals located inside the ellipsoid were considered as belonging to the homogeneous batch; those outside the ellipsoid were considered spurious. Results The PCA established eight descriptive axes that represented the accumulated variance of the data set in 88.71%. The allocation of the animals in the new system and the construction of the confidence region revealed six spurious animals as compared to the homogeneous batch of 109 animals. Conclusion The biometric criterion presented proved to be effective, because it considers the animal as a whole, analyzing jointly all parameters measured, in addition to having a small discard rate.

Genome-Wide Analysis in Brazilian Xavante Indians Reveals Low Degree of Admixture

Characterization of population genetic variation and structure can be used as tools for research in human genetics and population isolates are of great interest. The aim of the present study was to characterize the genetic structure of Xavante Indians and compare it with other populations. The Xavante, an indigenous population living in Brazilian Central Plateau, is one of the largest native groups in Brazil. A subset of 53 unrelated subjects was selected from the initial sample of 300 Xavante Indians. Using 86,197 markers, Xavante were compared with all populations of HapMap Phase III and HGDP-CEPH projects and with a Southeast Brazilian population sample to establish its population structure. Principal Components Analysis showed that the Xavante Indians are concentrated in the Amerindian axis near other populations of known Amerindian ancestry such as Karitiana, Pima, Surui and Maya and a low degree of genetic admixture was observed. This is consistent with the historical records of bottlenecks experience and cultural isolation. By calculating pair-wise F-st statistics we characterized the genetic differentiation between Xavante Indians and representative populations of the HapMap and from HGDP-CEPH project. We found that the genetic differentiation between Xavante Indians and populations of Ameridian, Asian, European, and African ancestry increased progressively. Our results indicate that the Xavante is a population that remained genetically isolated over the past decades and can offer advantages for genome-wide mapping studies of inherited disorders.

Understanding the correlates of adolescents' dietary intake patterns. A multivariate analysis

We investigated dietary intake patterns (DIP) in adolescents (14-18 year-olds) and the association with demographic and socioeconomic characteristics and lifestyle variables. This school-based survey was carried out among high school students from the city of Maringa in the state of Parana (PR), Brazil (2007). The sample included 991 students (54.5% girls) from high schools. DIPs were investigated by the frequency of weekly consumption of each food group: vegetables, fruit, rice, beans, fried food, sweet food, milk, soda, meat, eggs, alcoholic drinks. Independent variables were: demographic and socioeconomic characteristics and lifestyle variables. DIPS were identified using principal component analysis with orthogonal rotation (varimax). Three components were extracted. Component 1 (fried foods, sweets and soft drinks) was positively associated with not having breakfast for girls and dinner for boys. Moreover, component 2 (consumption of fruit and vegetables) was positively associated with having breakfast at home for boys and number of meals for girls. Component 3 (beans, eggs and meat) was positively associated with having lunch, employment and sedentary behavior level for girls. However, it was negatively associated with having lunch and dinner for boys. Adolescents who have healthier eating patterns also had other healthier behaviors regardless of gender. However, factors associated with dietary patterns differ between boys and girls. (C) 2012 Elsevier Ltd. All rights reserved.

FUNCTIONAL PRINCIPAL COMPONENTS MODEL FOR HIGH-DIMENSIONAL BRAIN IMAGING

We establish a fundamental equivalence between singular value decomposition (SVD) and functional principal components analysis (FPCA) models. The constructive relationship allows to deploy the numerical efficiency of SVD to fully estimate the components of FPCA, even for extremely high-dimensional functional objects, such as brain images. As an example, a functional mixed effect model is fitted to high-resolution morphometric (RAVENS) images. The main directions of morphometric variation in brain volumes are identified and discussed.

Application of stellar photometry to the analysis of microarray images

Improvements in the analysis of microarray images are critical for accurately quantifying gene expression levels. The acquisition of accurate spot intensities directly influences the results and interpretation of statistical analyses. This dissertation discusses the implementation of a novel approach to the analysis of cDNA microarray images. We use a stellar photometric model, the Moffat function, to quantify microarray spots from nylon microarray images. The inherent flexibility of the Moffat shape model makes it ideal for quantifying microarray spots. We apply our novel approach to a Wilms' tumor microarray study and compare our results with a fixed-circle segmentation approach for spot quantification. Our results suggest that different spot feature extraction methods can have an impact on the ability of statistical methods to identify differentially expressed genes. We also used the Moffat function to simulate a series of microarray images under various experimental conditions. These simulations were used to validate the performance of various statistical methods for identifying differentially expressed genes. Our simulation results indicate that tests taking into account the dependency between mean spot intensity and variance estimation, such as the smoothened t-test, can better identify differentially expressed genes, especially when the number of replicates and mean fold change are low. The analysis of the simulations also showed that overall, a rank sum test (Mann-Whitney) performed well at identifying differentially expressed genes. Previous work has suggested the strengths of nonparametric approaches for identifying differentially expressed genes. We also show that multivariate approaches, such as hierarchical and k-means cluster analysis along with principal components analysis, are only effective at classifying samples when replicate numbers and mean fold change are high. Finally, we show how our stellar shape model approach can be extended to the analysis of 2D-gel images by adapting the Moffat function to take into account the elliptical nature of spots in such images. Our results indicate that stellar shape models offer a previously unexplored approach for the quantification of 2D-gel spots. ^

Using hybrid latent class model for city-HUBs´users behaviour analysis

Data from an attitudinal survey and stated preference ranking experiment conducted in two urban European interchanges (i.e. City-HUBs) in Madrid (Spain) and Thessaloniki (Greece) show that the importance that City-HUBs users attach to the intermodal infrastructure varies strongly as a function of their perceptions of time spent in the interchange (i.e.intermodal transfer and waiting time). A principal components analysis allocates respondents (i.e. city-HUB users) to two classes with substantially different perceptions of time saving when they make a transfer and of time using during their waiting time.

Using the R package Shiny to create web applications that facilitate quantitative gene expression analysis

Thesis (Master's)--University of Washington, 2016-06

Cluster analysis of high-dimensional data: A case study

Normal mixture models are often used to cluster continuous data. However, conventional approaches for fitting these models will have problems in producing nonsingular estimates of the component-covariance matrices when the dimension of the observations is large relative to the number of observations. In this case, methods such as principal components analysis (PCA) and the mixture of factor analyzers model can be adopted to avoid these estimation problems. We examine these approaches applied to the Cabernet wine data set of Ashenfelter (1999), considering the clustering of both the wines and the judges, and comparing our results with another analysis. The mixture of factor analyzers model proves particularly effective in clustering the wines, accurately classifying many of the wines by location.

Quantifying the pathology of neurodegenerative disorders:Quantitative measurements, sampling strategies and data analysis

The use of quantitative methods has become increasingly important in the study of neurodegenerative disease. Disorders such as Alzheimer's disease (AD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This article reviews the advantages and limitations of the different methods of quantifying the abundance of pathological lesions in histological sections, including estimates of density, frequency, coverage, and the use of semiquantitative scores. The major sampling methods by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are also described. In addition, the data analysis methods commonly used to analyse quantitative data in neuropathology, including analyses of variance (ANOVA) and principal components analysis (PCA), are discussed. These methods are illustrated with reference to particular problems in the pathological diagnosis of AD and dementia with Lewy bodies (DLB).

Analysis of plasmid profiles of Aeromonas salmonicida isolates by pulsed field gel electrophoresis

Plasmid constitutions of Aeromonas salmonicida isolates were characterised by flat-bed and pulsed field gel electrophoresis. Resolution of plasmids by pulsed field gel electrophoresis was greater and more consistent than that achieved by flat-bed gel electrophoresis. The number of plasmids separated by pulsed field gel electrophoresis varied between A. salmonicida isolates, with five being the most common number present in the isolates used in this study. Plasmid profiles were diverse and the reproducibility of the distances migrated facilitated the use of principal components analysis for the characterisation of the isolates. Isolates were grouped according to the number of plasmids supported. Further principal components analysis of groups of isolates supporting five and seven plasmids showed a spatial separation of plasmids based upon distance migrated. Principal components analysis of plasmid profiles and antimicrobial minimum inhibitory concentrations could not be correlated suggesting that resistance to antimicrobial agents is not associated with either one plasmid or a particular plasmid constitution.

Evaluation of catalytic pyrolysis of cassava rhizome by principal component analysis

Rhizome of cassava plants (Manihot esculenta Crantz) was catalytically pyrolysed at 500 °C using analytical pyrolysis–gas chromatography/mass spectrometry (Py–GC/MS) method in order to investigate the relative effect of various catalysts on pyrolysis products. Selected catalysts expected to affect bio-oil properties were used in this study. These include zeolites and related materials (ZSM-5, Al-MCM-41 and Al-MSU-F type), metal oxides (zinc oxide, zirconium (IV) oxide, cerium (IV) oxide and copper chromite) catalysts, proprietary commercial catalysts (Criterion-534 and alumina-stabilised ceria-MI-575) and natural catalysts (slate, char and ashes derived from char and biomass). The pyrolysis product distributions were monitored using models in principal components analysis (PCA) technique. The results showed that the zeolites, proprietary commercial catalysts, copper chromite and biomass-derived ash were selective to the reduction of most oxygenated lignin derivatives. The use of ZSM-5, Criterion-534 and Al-MSU-F catalysts enhanced the formation of aromatic hydrocarbons and phenols. No single catalyst was found to selectively reduce all carbonyl products. Instead, most of the carbonyl compounds containing hydroxyl group were reduced by zeolite and related materials, proprietary catalysts and copper chromite. The PCA model for carboxylic acids showed that zeolite ZSM-5 and Al-MSU-F tend to produce significant amounts of acetic and formic acids.

Statistical analysis in microbiology:statnotes

This book is aimed primarily at microbiologists who are undertaking research and who require a basic knowledge of statistics to analyse their experimental data. Computer software employing a wide range of data analysis methods is widely available to experimental scientists. The availability of this software, however, makes it essential that investigators understand the basic principles of statistics. Statistical analysis of data can be complex with many different methods of approach, each of which applies in a particular experimental circumstance. Hence, it is possible to apply an incorrect statistical method to data and to draw the wrong conclusions from an experiment. The purpose of this book, which has its origin in a series of articles published in the Society for Applied Microbiology journal ‘The Microbiologist’, is an attempt to present the basic logic of statistics as clearly as possible and therefore, to dispel some of the myths that often surround the subject. The 28 ‘Statnotes’ deal with various topics that are likely to be encountered, including the nature of variables, the comparison of means of two or more groups, non-parametric statistics, analysis of variance, correlating variables, and more complex methods such as multiple linear regression and principal components analysis. In each case, the relevant statistical method is illustrated with examples drawn from experiments in microbiological research. The text incorporates a glossary of the most commonly used statistical terms and there are two appendices designed to aid the investigator in the selection of the most appropriate test.

Statnote 28:Canonical Variate Analysis (CVA)

The pattern of correlation between two sets of variables can be tested using canonical variate analysis (CVA). CVA, like principal components analysis (PCA) and factor analysis (FA) (Statnote 27, Hilton & Armstrong, 2011b), is a multivariate analysis Essentially, as in PCA/FA, the objective is to determine whether the correlations between two sets of variables can be explained by a smaller number of ‘axes of correlation’ or ‘canonical roots’.

Exploratory data analysis with non-linear and missing data in geochemistry

Exploratory analysis of data seeks to find common patterns to gain insights into the structure and distribution of the data. In geochemistry it is a valuable means to gain insights into the complicated processes making up a petroleum system. Typically linear visualisation methods like principal components analysis, linked plots, or brushing are used. These methods can not directly be employed when dealing with missing data and they struggle to capture global non-linear structures in the data, however they can do so locally. This thesis discusses a complementary approach based on a non-linear probabilistic model. The generative topographic mapping (GTM) enables the visualisation of the effects of very many variables on a single plot, which is able to incorporate more structure than a two dimensional principal components plot. The model can deal with uncertainty, missing data and allows for the exploration of the non-linear structure in the data. In this thesis a novel approach to initialise the GTM with arbitrary projections is developed. This makes it possible to combine GTM with algorithms like Isomap and fit complex non-linear structure like the Swiss-roll. Another novel extension is the incorporation of prior knowledge about the structure of the covariance matrix. This extension greatly enhances the modelling capabilities of the algorithm resulting in better fit to the data and better imputation capabilities for missing data. Additionally an extensive benchmark study of the missing data imputation capabilities of GTM is performed. Further a novel approach, based on missing data, will be introduced to benchmark the fit of probabilistic visualisation algorithms on unlabelled data. Finally the work is complemented by evaluating the algorithms on real-life datasets from geochemical projects.

Quantitative neuropathology:data collection and statistical analysis

The use of quantitative methods has become increasingly important in the study of neuropathology and especially in neurodegenerative disease. Disorders such as Alzheimer's disease (AD) and the frontotemporal dementias (FTD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This chapter reviews the advantages and limitations of the different methods of quantifying pathological lesions in histological sections including estimates of density, frequency, coverage, and the use of semi-quantitative scores. The sampling strategies by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are described. In addition, data analysis methods commonly used to analysis quantitative data in neuropathology, including analysis of variance (ANOVA), polynomial curve fitting, multiple regression, classification trees, and principal components analysis (PCA), are discussed. These methods are illustrated with reference to quantitative studies of a variety of neurodegenerative disorders.